The Augmented Matrix Is Given for a System of Equations $$\left[ \begin{array} { r r r r } 1 & 2 & - 3 & 5 \\0 & 1 & 4 & - 5 \\0 & 0 & 0 & 0\end{array} \right]$$

question 13

Multiple Choice

The augmented matrix is given for a system of equations. If the system is consistent, find the general solution.
Otherwise state that there is no solution.
- $$\left[ \begin{array} { r r r r } 1 & 2 & - 3 & 5 \\0 & 1 & 4 & - 5 \\0 & 0 & 0 & 0\end{array} \right]$$

• A) \(x _ { 1 } = 5 - 2 x _ { 2 } + 3 x _ { 3 }\)
• \(x _ { 2 } = - 5 - 4 x _ { 3 }\)
• \(x _ { 3 }\) is free
• B) \(x _ { 1 } = 5 - 2 x _ { 2 } + 3 x _ { 3 }\)
• \(x _ { 2 }\) is free
• \(x _ { 3 }\) is free
• C) \(x _ { 1 } = 15 + 11 x _ { 3 }\)
• \(x _ { 2 } = - 5 - 4 x _ { 3 }\)
• \(x _ { 3 } = 0\)
• D) \(x _ { 1 } = 15 + 11 x _ { 3 }\)
• \(x _ { 2 } = - 5 - 4 x _ { 3 }\)
• \(x _ { 3 }\) is free

Recognize different statistical terms and their definitions (e.g., degrees of freedom, frequencies, z-score).

Know the difference between descriptive and inferential statistics.

Differentiate between different types of data (categorical vs. continuous) and understand why the distinction is important.

Identify and explain the purposes of basic statistical tests (e.g., chi-square test).

---

Definitions:

Simplify

To make something less complex or complicated, making it easier to understand or solve.

Radical

Refers to the root of a number, with the most common being the square root, though it can refer to cube roots or higher.

Square Root

A number which produces a specified quantity when multiplied by itself.

Square Root

The figure that, upon being multiplied with itself, results in the starting number.